A288068 Repdigits in base 10 which are Brazilian numbers.

7, 8, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 444, 555, 666, 777, 888, 999, 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999, 11111, 22222, 33333, 44444, 55555, 66666, 77777, 88888, 99999, 111111, 222222, 333333, 444444, 555555, 666666, 777777, 888888, 999999

Offset: 1

Author

Bernard Schott, Jun 05 2017

Keywords

• nonn
• base

Comments

These numbers are all repdigits belonging to A010785. The representation of the numbers 7 and 8 in base 10 is not Brazilian but they are yet Brazilian because 7 = 111_2 and 8 = 22_3. Except the repdigits 7, 8, 22, 33, 55, 77 and the primes repunits R_n from A004022 and A004023, all these Brazilian repdigits are also Brazilian in another base.

Contains all base-10 repdigits (A010785) >= 22, because these are Brazilian numbers in base 10. - R. J. Mathar, Jul 19 2024

Examples

			7 = 111_2;
44 = 44_10 = 22_21;
66 = 66_10 = 33_21 = 22_32.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, -10).

Crossrefs

Cf. A004022, A004023, A010785, A014181, A125134,

Programs

Maple

# reuses code of A125134, b-file output
n := 1 :
for ndigs from 1 do
    for d from 1 to 9 do
        r := add(d*10^i,i=0..ndigs-1) ; # rep digit d in base 10
        if isA125134(r) then
            printf("%d %d\n",n,r) ;
            n := n+1 ;
        end if;
    end do:
end do: # R. J. Mathar, Jul 19 2024

Mathematica

Select[Flatten@ Table[FromDigits@ ConstantArray[k, n], {n, 6}, {k, 9}], Function[n, Length@ SelectFirst[Range[2, n - 2], Count[DigitCount[n, #], ?(# > 0 &)] == 1 &] == 0]] (* _Michael De Vlieger, Jun 06 2017, Version 10 *)